有理空间的自同态等价群不能是自由阿贝尔群

Pub Date : 2022-05-13 DOI:10.2969/jmsj/87158715

M. Benkhalifa

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引用次数: 4

摘要

在本文中，我们证明了自由阿贝尔群不能作为有限型有理CW复形的自同态等价群出现。因此，我们推广了Sullivan Wilkerson的一个结果，证明了如果X是有限类型的有理CW复形，使得dimH*（X，Z）<∞或dimπ*（X）<∞，那么X的自同构等价群同构于在Q上定义的线性代数群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The group of self-homotopy equivalences of a rational space cannot be a free abelian group

In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dimH∗(X,Z) < ∞ or dimπ∗(X) < ∞, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.

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